In a right-angled triangle OAD with a hypotenuse AD, the angle A = 60 degrees. From the vertex O

In a right-angled triangle OAD with a hypotenuse AD, the angle A = 60 degrees. From the vertex O, the height OK is dropped. What is the side KD if AK = 5cm.

Since OK is the height, the triangles OKD and OKA are rectangular. The AOK angle of the OKA triangle is equal to: AOK = (90 – 60) = 30.

Leg AK = 5 cm and erect against an angle of 30, then OA = 2 * AK = 10 cm.

By the Pythagorean theorem, OK ^ 2 = OA ^ 2 – AK ^ 2 = 100 – 25 = 75.

OK = 5 * √3 cm.

Angle ODA = (90 – 60) = 30, then the leg OK lies opposite the angle 30, then OD = 2 * OK = 10 * √3 cm, then KD ^ 2 = OD ^ 2 – OK ^ 2 = 300 – 75 = 225 …

КD = 15 cm.

Answer: The length of the segment KD is 15 cm.